Consistent pricing of bivariate interest rate exotics via constrained Schrödinger optimal transport

Battle Count: 78

The paper is primarily relevant to derivatives desk pricing and risk management rather than algorithmic trading or portfolio construction. It addresses a specific niche in interest rate derivatives (bivariate CMS exotics) and provides tools for consistent pricing and no-arbitrage bound computation. While valuable for quantitative analysts at banks and trading desks dealing with exotic interest rate products, it has limited direct applicability to systematic trading strategies or broader quantitative finance applications.

Implementation requires: (1) discretization of continuous distributions via Gauss-Legendre quadrature, (2) construction of prior joint density from copula and marginal densities, (3) solving a concave optimization problem with explicit Jacobian and Hessian using damped Newton method, (4) adaptive epsilon scheduling for numerical stability at small epsilon, (5) handling the spread constraint structure D_k, and (6) careful management of exponential terms to avoid overflow/underflow. The mathematical sophistication is high, involving optimal transport theory, Lagrangian duality, and Bregman projections. However, the final optimization is a standard gradient-based problem once the dual is formulated.

The paper provides detailed mathematical formulations, algorithmic steps (dual Lagrangian, adaptive epsilon scheduling, Gauss-Legendre discretization), and numerical examples with specific parameters (n=m=200, 20 strikes, epsilon values). However, no code repository is provided, and market data used for calibration is not publicly available. The methodology is well-described enough for an expert to reimplement, but practical reproduction requires proprietary market data.